Yahoo Finance stock price analysis

Apple Inc.

Grzegorz Chadysz, Konrad ArchiciƄski

01.06.2021


Introduction

This R Markdown report enables to analyze time series from Yahoo Finance of user’s choice. The report takes user input and creates tables, plots and tests based on that input and allows to thoroughly analyze different quotes and time spans without interfering with the code.

This version of report provides several tech and motor companies to choose from, however, should one want to analyze another, he/she should add the abbreviation and company’s full name to the parameter’s choice list and dictionary and the report would be good to go. Default time range spans back a thousand days from the day of running the report. Should the multiple choice for the quotes be left empty, then as default, all prices are included in the analysis. Last parameter determines the forecast period in days.


Data

Gathering of the time series data is performed via getSymbols function provided in quantmod package. More information about the package can be found here. Data used in this particular report is characterized by following parameters:

  • Company name: Apple Inc.
  • Company abbreviation: AAPL
  • Time span: 2021-03-29 - 2021-06-01
  • Quotes: Low, Close
  • Simulation paths: 10

Below you can see a glimpse of the first and last few observations of the data of your choice.

Most recent observations
Date AAPL.Low AAPL.Close
2021-05-28 124.55 124.61
2021-05-27 125.08 125.28
2021-05-26 126.42 126.85
2021-05-25 126.32 126.90
2021-05-24 125.94 127.10
2021-05-21 125.21 125.43
Oldest observations
Date AAPL.Low AAPL.Close
2021-04-06 125.65 126.21
2021-04-05 123.07 125.90
2021-04-01 122.49 123.00
2021-03-31 121.15 122.15
2021-03-30 118.86 119.90
2021-03-29 120.73 121.39

Descriptive statistics

General

Below you can find a handful of descriptive statistics regarding the columns specified during knitting. Maximum price recorded for Apple Inc. during 2021-03-29 - 2021-06-01 period was $134.84, while the minimum was $4.15. Number of observations between the periods is equal to 44.

Stats per variable
Variable Mean Std. Min 1st quartile Median 3rd quartile Max
AAPL.Low 127.66 4.15 118.86 125.01 126.75 131.70 134.11
AAPL.Close 128.80 4.23 119.90 125.78 127.88 133.03 134.84

Log returns

This chapter provides insight on the log returns of selected prices. Log returns are more widely used in finance than simple returns for a number of reasons, one being that prices are assumed to be log-normally distributed. That is not always the case as can be seen on the graphs below. Nevertheless, this assumption results in logarithms of prices to be normally distributed. More information on this topic can be found here.

Each of the graphs below represents a histogram of log returns of certain price, as well as kernel density estimate (white line). It is plotted agains a normal distribution (red line) with mean and standard deviation calculated separately for each graph.

AAPL.Low

AAPL.Close


Plotting

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Stationarity analysis

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Trend

## 
## ############################################### 
## # Augmented Dickey-Fuller Test Unit Root Test # 
## ############################################### 
## 
## Test regression trend 
## 
## 
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + tt + z.diff.lag)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9673 -0.8155  0.0528  0.9259  2.5893 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.93095    0.60096   1.549  0.12987    
## z.lag.1     -0.99103    0.23912  -4.144  0.00019 ***
## tt          -0.03856    0.02394  -1.611  0.11573    
## z.diff.lag  -0.08178    0.15775  -0.518  0.60724    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.68 on 37 degrees of freedom
## Multiple R-squared:  0.5489, Adjusted R-squared:  0.5123 
## F-statistic:    15 on 3 and 37 DF,  p-value: 1.507e-06
## 
## 
## Value of test-statistic is: -4.1445 5.7455 8.5908 
## 
## Critical values for test statistics: 
##       1pct  5pct 10pct
## tau3 -4.15 -3.50 -3.18
## phi2  7.02  5.13  4.31
## phi3  9.31  6.73  5.61


According to the ADF test the series are integrated of order 1, or in other words have become stationary after 1 differentiation(s). The program differentiated the series until it found order where value of test-statistic: -4.1444584 is smaller than tau3 5pct: -3.5.


Drift

## 
## ############################################### 
## # Augmented Dickey-Fuller Test Unit Root Test # 
## ############################################### 
## 
## Test regression drift 
## 
## 
## Call:
## lm(formula = z.diff ~ z.lag.1 + 1 + z.diff.lag)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.0039 -0.6813  0.1793  1.0913  2.9578 
## 
## Coefficients:
##             Estimate Std. Error t value Pr(>|t|)    
## (Intercept)  0.06163    0.26984   0.228 0.820577    
## z.lag.1     -0.84750    0.22651  -3.742 0.000603 ***
## z.diff.lag  -0.14187    0.15646  -0.907 0.370257    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.715 on 38 degrees of freedom
## Multiple R-squared:  0.5172, Adjusted R-squared:  0.4918 
## F-statistic: 20.36 on 2 and 38 DF,  p-value: 9.8e-07
## 
## 
## Value of test-statistic is: -3.7416 7.0262 
## 
## Critical values for test statistics: 
##       1pct  5pct 10pct
## tau2 -3.58 -2.93 -2.60
## phi1  7.06  4.86  3.94


According to the ADF test the series are integrated of order 1, or in other words have become stationary after 1 differentiation(s). The program differentiated the series until it found order where value of test-statistic: -3.7416081 is smaller than tau3 5pct: -2.93.


None

## 
## ############################################### 
## # Augmented Dickey-Fuller Test Unit Root Test # 
## ############################################### 
## 
## Test regression none 
## 
## 
## Call:
## lm(formula = z.diff ~ z.lag.1 - 1 + z.diff.lag)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9407 -0.6300  0.2296  1.1462  3.0134 
## 
## Coefficients:
##            Estimate Std. Error t value Pr(>|t|)    
## z.lag.1     -0.8412     0.2221  -3.788 0.000513 ***
## z.diff.lag  -0.1449     0.1540  -0.941 0.352643    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.694 on 39 degrees of freedom
## Multiple R-squared:  0.517,  Adjusted R-squared:  0.4922 
## F-statistic: 20.87 on 2 and 39 DF,  p-value: 6.88e-07
## 
## 
## Value of test-statistic is: -3.788 
## 
## Critical values for test statistics: 
##       1pct  5pct 10pct
## tau1 -2.62 -1.95 -1.61


According to the ADF test the series are integrated of order 1, or in other words have become stationary after 1 differentiation(s). The program differentiated the series until it found order where value of test-statistic: -3.7880011 is smaller than tau3 5pct: -1.95.


Simulation

ARMA(1,1)-GARCH(1,1)

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